Subdomain Settings

Step 5 Choose Physics/Subdomain Settings, and click on subdomain 1. Set the parameters as follows. 

Step 6 Choose Physics/Subdomain Settings and select 1. Insert the following values and click OK ... 

Step 12 Choose Options/Expressions/Subdomains/. Set the following expressions ... 

Step 4 Specify the parameters for the differential equation. Choose Physics/Subdomain Settings to see the equation ... 

Step 4 In the menu Phy sics/Subdomain Settings set the following values, as shown in Figure 9.9. 

Figure 9.9. Subdomain Settings for cylindrical geometry in one dimension.

One handy way to get all the solutions for several pressure drops (and avoid convergence problems) is to use the Parametric Nonlinear option in the Solver Parameters. Call the variable presdropx and set its value to 0 1 7. Then in the Physics/Subdomain Settings, where you put the Ap, replace it with lO presdropx. The program FEMLAB... 

Step 4 In the Physics/Subdomain Settings mode the equation listed at the top is... 

Step 4 Be sure the concentration equation is selected (under the Multiphysics menu). Under the Physics/Subdomain Settings, the following equation is displayed ... 

Step 3 Under the Physics/Subdomain Settings, the following equation is displayed. 

Step 5 Choose Physics/Subdomain Settings and a window appears showing Eq. (10.10) ... 

Step 2 If the variable used for viscosity is eta, then under the Physics/Subdomain Settings, you insert the word eta is inserted in the box for 17. That is all that is required to set up the non-Newtonian problem. As the problem is being solved, when the viscosity... 

Step 3 You solve for properties appropriate to water (p = 1000 kg/m p, = 0.001 Pa s) in a small pipe with a diameter of 0.005 m. The applied pressure drop is taken as 100 Pa/ m. At steady state, the average velocity should then be 0.078 m/s, using Eq. (9.9). Under Subdomain Settings, put in the parameters. Then click the Tnit tab and be sure that the velocity is initially zero. 

Step 4 Next set the parameters in the differential equation. Choose Physics/Subdomain Settings, and select domain 1. A window appears with Eq. (11.29) at the top. For this problem, you change to k = 1 but leave the other variables set to zero. Click OK. 

Step 2 Note that when you are setting domain parameters or boundary conditions, you do this only one equation at a time, and you have to select the equation you want under the Multiphysics tab. Select the convection and diffusion equation. Then, select Physics/Subdomain Settings, leave Disotropic = 1, and R = Q (this can be a reaction rate depending upon c). In the u and v boxes, put u and v, respectively otherwise convection will be absent from the problem. 

Step 1 Choose the Navier-Stokes equation under the Multiphysics/Model Navigator option. Then choose Physics/Subdomain Settings. Select the domain and type in the formula for viscosity 1 -I- c. If you have several concentration variables, be sure to use the variable names assigned by FEMLAB (or changed by you) in this formula. 

Step 2 Under Physics/Subdomain Settings, insert the following equation for Q, the heat generation term. The notation is changed to use u as the radial velocity and v as the axial velocity. 

Equation (11.38) is inserted for the viscosity for the Physics/Subdomain Settings for the Navier-Stokes equation ... 

Step 2 Under Physics/Subdomain Settings, select the domain and enter the reaction rate in the window for R, the reaction rate. The equation listed at the top is... 

Next you would define the parameters in the differential equation. Choose the Physics menu at the top, and go down to Subdomain Settings. The screen appears as shown in Figure D.6. At the top is the equation that will be solved. Once a subdomain is selected (here the 1), you can change the parameters in the boxes. If you have more than one sub-domain (perhaps two regions with different physical properties), there would be at least two numbers here and you could set the parameters for each region separately (or together). 

Step 5 Make sure Geom2 is selected and set the parameters and boundary conditions under Physics/Subdomain Settings and Physics/Boundary Settings. For Boundary 1, choose fte boundary condition Temperature and type in tout. 

Defining a COMSOL application mode consists of three parts the application mode selection with dependent variable declaration, the boundary settings, and the subdomain settings. In our case, the application mode is diffusion of dilute species from the chemical engineering module ... 

The final step to defining a COMSOL application mode is to set the subdomain settings. Similarly to how BulkConc and SurfReact were defined in MATLAB for the boundary conditions, DiffCoef, BflmReact, and InitConc would also all need to be defined as three-element arrays in MATLAB, with each element corresponding to the dependent variable of interest (S, M, and M ). 

It is often desired to add a differential equation in COMSOL that is not available through one of their built-in application modes. For example, in our model, we wanted to add a custom PDF to calculate the redox potential drop through the biofilm via Ohm s law Equation 9.21. To achieve this, we use the generic PDE application mode. As in the built-in application modes, defining a custom PDE application mode consists of the application mode selection, boundary settings, and subdomain settings. However, in the generic PDE application mode, we must also define the PDE itself. For the coefficient form, which is used in this case, the PDE takes the form of ... 

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